This lesson from the ‘Number’ section of GCSE Maths is all about Lowest Common Multiples, and using Prime Factors to help find them (transcript below video).

In this section, we’re going to look at the Lowest Common Multiple of two numbers. This is the smallest number that is in both of the times tables, of the two numbers. The first thing you want to do is write down the times tables of the numbers that you’re given. For example, if you’re having to find the Lowest Common Multiple of 3 and 4, you would write down their times tables.

For 3, you would have; 3, 6, 9, 12, 15 and 18. We can stop there for now.

For 4, you would have; 4, 8, 12, 16, 20 and that carries on…

We don’t need to write out our times tables any further as you can see we already have a common number between the two, which is 12. This is the smallest common number between the times tables, which means the Lowest Common Multiple between 3 and 4 is 12. There is another method you can use, which involves using the prime factors of each number, which we looked at in the previous section. I will talk you through this method in an example exam question.

Here is an example of a typical exam question you might get involving Lowest Common Multiples. I’m going to show you how to solve it using Prime Factors. We have already looked at how to find prime factors using a factor tree. This is in one of the earlier lessons, if you would like to revise that first. Now, assuming we already know how to do this, we can write the prime factors out of these two numbers.

For 28, we can write out our prime factors as; 2 x 2 x 7.

For 8, we can write out our prime factors as; 2 x 2 x 2.

Now you need to write these prime factors out in a Venn Diagram (which we have drawn below). On one side we have all the factors of 28, with all the factors of 8 on the right hand side. The section in the middle will include any factors that are common to both. Here, ‘2 x 2’ is common between both numbers. This means you write both of these in the middle section. For 28, we are left with a 7, which goes in the left hand side. For 8, we are left with one more 2, which will go in to the right hand side section.

Lastly, to find the Lowest Common Multiple, you multiply together all of the numbers that are written on your Venn Diagram. In our example, we have 7, 2, 2 and 2 written down in our diagram. This means our Lowest Common Multiple between 28 and 8 will be: 7 x 2 x 2 x 2 = 56.

Thanks for watching, and if you have any questions about the topics talked about, or you are stuck on a particular concept, just get in touch and we will get back to you as soon as possible!